BB84 Time-bin Simulation

This repository contains a Python script that simulates detection events in a quantum key distribution (QKD) experiment using the BB84 protocol with time-bin encoding.

The simulation is designed for educational purposes and can be used as a basis for laboratory exercises in quantum optics or quantum information.

📋 Overview

The script generates a list of timestamped detection events resulting from a BB84 time-bin setup. It includes:

• Random bit and basis generation for Alice and Bob
• Time-of-arrival based detection (Z basis)
• Interference-based detection (X basis)
• Gaussian timing jitter to simulate realistic detector response
• Background noise events (uncorrelated random detections)
• Final histogram plotting of detection events within a single quantum state window (two time-bins)

The output simulates what an experiment might produce, and can be analyzed to extract bit values, sift keys, calculate QBER or visibility, and extract secure key rate.

📂 Files

• generate_data.py — The main script that generates and plots detection events

▶️ How to Run

This script requires Python 3 and the following packages:

• numpy
• matplotlib

You can install the dependencies with:

pip install numpy matplotlib

Then run the script:

python generate_data.py

🛠️ Parameters and Output Structure

Adjustable Parameters

The following parameters can be modified at the top of the script to explore different simulation conditions:

Parameter	Description	Default Value
num_states	Number of quantum states sent by Alice (i.e., number of time-bins)	100000
state_duration	Duration of each time-bin (in seconds)	2e-9 (2 ns)
bin_offset	Time separation between early and late bins (defines the qubit encoding)	1e-9 (1 ns)
jitter_std	Standard deviation of Gaussian timing jitter (simulates detector noise)	40e-12 (40 ps)
num_noise_events	Number of uncorrelated background noise events	10000

These parameters affect the density of events, temporal resolution, and signal-to-noise ratio in the output.

Encoding Variables

The quantum information in the simulation is encoded through the following arrays:

Variable	Shape	Description
alice_bases	(num_states,)	Basis chosen by Alice for each qubit: 0 = Z, 1 = X
alice_bits	(num_states,)	Bit chosen by Alice to encode: 0 or 1
bob_bases	(num_states,)	Basis chosen by Bob for measurement: 0 = Z, 1 = X

These arrays define the ideal quantum communication process:

• If alice_bases[i] == bob_bases[i], the measurement is meaningful (i.e., they used the same basis).
• If the bases differ, the result is random, as in real QKD.

These variables are not directly included in the final timestamps array, but can be used to analyze QBER (Quantum Bit Error Rate) or visibility of interference. If you plan to use these arrays for downstream analysis, you can save them using numpy.save() or numpy.savez() for later loading.

Output: timestamps array

The final output of the simulation is stored in a NumPy array called timestamps, which is a 2D array with shape (N, 2):

timestamps[i, 0] → timestamp in seconds (float); timestamps[i, 1] → detector number (1, 2, or 3)

• Detector 1: Time-of-arrival detection (Z basis)
• Detector 2/3: Time of interferometric detection (X basis), distinguishing phase 0 vs π
• The timestamps are sorted chronologically.
• Noise events are randomly interleaved and indistinguishable from valid detections without additional metadata.